Problem: Solve for $x$ and $y$ using elimination. ${2x-4y = 10}$ ${-2x+3y = -11}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {2x-4y = 10}\thinspace$ to find $x$ ${2x - 4}{(1)}{= 10}$ $2x-4 = 10$ $2x-4{+4} = 10{+4}$ $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ You can also plug ${y = 1}$ into $\thinspace {-2x+3y = -11}\thinspace$ and get the same answer for $x$ : ${-2x + 3}{(1)}{= -11}$ ${x = 7}$